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User blog:DaRKMaRoWaK/A Tiny Fact
You may not have wondered about it, but have you ever thought of how many type of matches you can make in a level in 1 move? NOTE:I'm only including for 1 move only and no matches to be present after the candy has filled up the spots of the already matched candy. Let's take level 1 as an example: As you can see, this level includes a 8x5 rectangular box consisting of 40 candy. So let's not look at the candy's positions. We'll imagine where their positions are when we count it, Before we start, you should first know about how big the box of candies are involved when making a match. Making a 3 candy match would involve either a 1x4 or a 2x3 box. The 1x4 box involves 3 possible matches while the 2x3 box involves 6 possible matches. (Adding 3 more if 2 candy matches are formed from that 1 move, but we'll count that later) So let's start with the 1x4 box first. (8-4+1)*(5-1+1)=5*5 :=25 While if we rotate it: (8-1+1)*(5-4+1)=8*2 :=16 So, 3(25+16)=3(41) =123 Now with the 2x3 box: (8-2+1)*(5-3+1)=7*3 :=21 Rotate it: (8-3+1)*(5-2+1)=6*4 :=24 So, 6(21+24)=6(45) =270 Conclusion, we can make 123+270=393 types of 3-candy matches. Now we move on to the 4-candy matches. Theirs are similar, but only with a 2x4 box, which you can make only 4 types of matches per box. (You should probably be able to figure out how they look like) With the 2x4 box: (8-2+1)*(5-4+1)=7*2 :=14 Rotate it: (8-4+1)*(5-2+1)=5*4 :=20 Conclusion, we can make 4(14+20)=4(34) =136 types of 4-candy matches. For 5-candy matches, they are similar, but has lesser possibilities unlike the rest. Like 4-candy matches, their boxes are only 2x5 boxes, with only 2 matches in them. With the 2x5 box: (8-2+1)*(5-5+1)=7*1 :=7 Rotate it: (8-5+1)*(5-2+1)=4*4 :=16 Conclusion, we can make 2(7+16)=2(23) =46 types of 5-candy matches. Add them all up and you get 393+136+46=575 types of matches, but that's not the final answer. Since we can also make multiple 3-candy matches, 4-candy matches or 5-candy matches with 1 move. (Still notice the Note message) There are 6 types, which include: *3+3 candy *3+4 candy *3+5 candy *4+4 candy *4+5 candy *5+5 candy We'll start with the first one, which is 3+3 candy. They can be made with either a 1x6 box (1 match), a 2x5 box (includes 2x3 (9=3*3), 2x4 (4=2*2) and 2*5 (2=2*1)=15 matches) or a 3x4 box. (6 matches) With the 1x6 box: (8-6+1)*(5-1+1)=3*5 :=15 Of course, you cannot rotate it. With the 2x3 box: (8-2+1)*(5-3+1)=7*3 :=21 Rotate it: (8-3+1)*(5-2+1)=6*4 :=24 So, 9(21+24)=9(45) =405 With the 2x4 box: (8-2+1)*(5-4+1)=7*2 :=14 Rotate it: (8-4+1)*(5-2+1)=5*4 :=20 So, 4(14+20)=4(34) =136 With the 2x5 box: (8-2+1)*(5-5+1)=7*1 :=7 Rotate it: (8-5+1)*(5-2+1)=4*4 :=16 So, 2(7+16)=2(23) =46 With the 3x4 box: (8-3+1)*(5-4+1)=6*2 :=12 Rotate it: (8-4+1)*(5-3+1)=5*3 :=15 So, 6(12+15)=6(27) =162 Conclusion, we can make 15+405+136+46+162=764 3+3 candy matches. Since the rest of the process is too long for this blog, they will not be written here and I shall write in the final answer at the bottom. After counting, the final total is... 4175! Category:Blog posts